A203483 a(n) = v(n+1)/v(n), where v = A203482.

3, 56, 19500, 267841728, 236189890379520, 19303349192505048268800, 199126474924007956512865886208000, 339543987407937097660189431863908761600000000, 121553118121801544803671246298148699436481551316864204800000

Offset: 1

Author

Clark Kimberling, Jan 03 2012

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..29

Crossrefs

Cf. A000142, A093883, A203482, A203510, A323717.

Programs

Magma

[(&*[Factorial(k) + Factorial(n+1): k in [1..n]]): n in [1..16]]; // G. C. Greubel, Aug 29 2023

Mathematica

(* First program *)
f[j_]:= j!; z = 10;
v[n_]:= Product[Product[f[k] + f[j], {j,k-1}], {k,2,n}]
d[n_]:= Product[(i-1)!, {i, n}]   (* A000178 *)
Table[v[n], {n,z}]                (* A203482 *)
Table[v[n+1]/v[n], {n,z-1}]       (* this sequence *)
Table[v[n]/d[n], {n,10}]          (* A203510 *)
(* Second program *)
Table[Product[k!+(n+1)!, {k,n}], {n,15}] (* G. C. Greubel, Aug 29 2023 *)

SageMath

[product(factorial(k) + factorial(n+1) for k in range(1,n+1)) for n in range(1,16)] # G. C. Greubel, Aug 29 2023

Formula

a(n) = Product_{k=1..n} (k! + (n+1)!). - G. C. Greubel, Aug 29 2023

From Vaclav Kotesovec, Nov 20 2023: (Start)

a(n) ~ (n+1)!^n.

a(n) ~ (2*Pi)^(n/2) * n^(n^2 + 3*n/2) / exp(n^2 - 13/12). (End)